2,352 research outputs found
How to detect level crossings without looking at the spectrum
We remind the reader that it is possible to tell if two or more eigenvalues
of a matrix are equal, without calculating the eigenvalues. We then use this
property to detect (avoided) crossings in the spectra of quantum Hamiltonians
representable by matrices. This approach provides a pedagogical introduction to
(avoided) crossings, is capable of handling realistic Hamiltonians
analytically, and offers a way to visualize crossings which is sometimes
superior to that provided by the spectrum. We illustrate the method using the
Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground
state hydrogen atom in a uniform magnetic field.Comment: Accepted for publication in the American Journal of Physic
A hadron model with breaking of spatial homogeneity of vacuum
A possible breaking of spatial homogeneity of vacuum due to the interaction
between quark and Bose-field is analyzed. It is shown that in this case quark
can be in a localized state (like wave packet). Energetic conditions for such a
spontaneous symmetry breaking are found in suggested model. Possible
consequences of such symmetry breaking, in particular, the origin of deep
inelastic processes and quark confinement phenomenon are discussed.Comment: 4 page
Odd Parity and Line Nodes in Non-Symmorphic Superconductors
Group theory arguments have been invoked to argue that odd parity order
parameters cannot have line nodes in the presence of spin-orbit coupling. In
this paper we show that these arguments do not hold for certain non-symmorphic
superconductors. Specifically, we demonstrate that when the underlying crystal
has a twofold screw axis, half of the odd parity representations vanish on the
Brillouin zone face perpendicular to this axis. Many unconventional
superconductors have non-symmorphic space groups, and we discuss implications
for several materials, including UPt3, UBe13, Li2Pt3B and Na4Ir3O8.Comment: 4 page
Optical injection and terahertz detection of the macroscopic Berry curvature
We propose an experimental scheme to probe the Berry curvature of solids. Our
method is sensitive to arbitrary regions of the Brillouin zone, and employs
only basic optical and terahertz techniques to yield a background free signal.
Using semiconductor quantum wells as a prototypical system, we discuss how to
inject Berry curvature macroscopically, and probe it in a way that provides
information about the underlying microscopic Berry curvature.Comment: 4 pages, accepted in Physical Review Letter
Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass
We study the behaviour of the expectation value of the acceleration of a
particle in a one-dimensional periodic potential when an external homogeneous
force is suddenly applied. The theory is formulated in terms of modified Bloch
states that include the interband mixing induced by the force. This approach
allows us to understand the behaviour of the wavepacket, which responds with a
mass that is initially the bare mass, and subsequently oscillates around the
value predicted by the effective mass. If Zener tunneling can be neglected, the
expression obtained for the acceleration of the particle is valid over
timescales of the order of a Bloch oscillation, which are of interest for
experiments with cold atoms in optical lattices. We discuss how these
oscillations can be tuned in an optical lattice for experimental detection.Comment: 15 pages, 12 figure
``Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields
We present some consequences of non-anomalous propagation requirements on
various massless fields. Among the models of nonlinear electrodynamics we show
that only Maxwell and Born-Infeld also obey duality invariance. Separately we
show that, for actions depending only on the F_\mn^2 invariant, the permitted
models have . We also characterize acceptable
vector-scalar systems. Finally we find that wide classes of gravity models
share with Einstein the null nature of their characteristic surfaces.Comment: 11 pages, LaTeX, no figure
Time evolution and squeezing of the field amplitude in cavity QED
We present the conditional time evolution of the electromagnetic field
produced by a cavity QED system in the strongly coupled regime. We obtain the
conditional evolution through a wave-particle correlation function that
measures the time evolution of the field after the detection of a photon. A
connection exists between this correlation function and the spectrum of
squeezing which permits the study of squeezed states in the time domain. We
calculate the spectrum of squeezing from the master equation for the reduced
density matrix using both the quantum regression theorem and quantum
trajectories. Our calculations not only show that spontaneous emission degrades
the squeezing signal, but they also point to the dynamical processes that cause
this degradation.Comment: 12 pages. Submitted to JOSA
Singularities and the distribution of density in the Burgers/adhesion model
We are interested in the tail behavior of the pdf of mass density within the
one and -dimensional Burgers/adhesion model used, e.g., to model the
formation of large-scale structures in the Universe after baryon-photon
decoupling. We show that large densities are localized near ``kurtoparabolic''
singularities residing on space-time manifolds of codimension two ()
or higher (). For smooth initial conditions, such singularities are
obtained from the convex hull of the Lagrangian potential (the initial velocity
potential minus a parabolic term). The singularities contribute {\em
\hbox{universal} power-law tails} to the density pdf when the initial
conditions are random. In one dimension the singularities are preshocks
(nascent shocks), whereas in two and three dimensions they persist in time and
correspond to boundaries of shocks; in all cases the corresponding density pdf
has the exponent -7/2, originally proposed by E, Khanin, Mazel and Sinai (1997
Phys. Rev. Lett. 78, 1904) for the pdf of velocity gradients in one-dimensional
forced Burgers turbulence. We also briefly consider models permitting particle
crossings and thus multi-stream solutions, such as the Zel'dovich approximation
and the (Jeans)--Vlasov--Poisson equation with single-stream initial data: they
have singularities of codimension one, yielding power-law tails with exponent
-3.Comment: LATEX 11 pages, 6 figures, revised; Physica D, in pres
On linearization of super sine-Gordon equation
Two sets of super Riccati equations are presented which result in two linear
problems of super sine-Gordon equation. The linear problems are then shown to
be related to each other by a super gauge transformation and to the super
B\"{a}cklund transformation of the equation.Comment: 9 Page
- …